The spin quantum number ms

The fourth quantum number is the spin quantum number (ms) and indicates the direction the electron is spinning. There are only two possible values for ms, + V2 and —V2. When two electrons are to occupy the same orbital, then one must have an ms = +V2 and the other electron must have an ms = -V2. These are spin-paired electrons. 

The spin quantum number, ms, describes the spin of the electron and can only have values of +/ and —A. 

Assume that the rules for quantum numbers are different and that the spin quantum number ms can have any of three values, ms = —1/2, 0, +1/2, while all other rules remain the same. 

The only quantum number that flows naturally from the Bohr approach is the principal quantum number, n the azimuthal quantum number Z (a modified k), the spin quantum number ms and the magnetic quantum number mm are all ad hoc, improvised to meet an experimental reality. Why should electrons move in elliptical orbits that depend on the principal quantum number n Why should electrons spin, with only two values for this spin Why should the orbital plane of the electron take up with respect to an external magnetic field only certain orientations, which depend on the azimuthal quantum number All four quantum numbers should follow naturally from a satisfying theory of the behaviour of electrons in atoms. 

Slater determinants enforce the Pauli exclusion principle, which forbids any two electrons in a system to have all quantum numbers the same. This is readily seen for an atom if the three quantum numbers n, l and mm of ij/(x, y, z) (Section 4.2.6) and the spin quantum number ms of a or /i were all the same for any electron, two rows (or columns, in the alternative formulation) would be identical and the determinant, hence the wavefunction, would vanish (Section 4.3.3). 

The spin quantum number ms or s has one of two possible values -1/2 or +1/2. ms differentiates between the two possible electrons occupying an orbital. Electrons moving through a magnet behave as if they were tiny magnets themselves spinning on their axis in either a clockwise or counterclockwise direction. These two spins may be described as ms = -1/2 and +1/2 or as down and up. 

In addition to the three quantum numbers used to describe the one-electron wave function, the electron has also a fourth, the spin quantum number, ms. It is related to the intrinsic angular momentum of the electron, called spin. This quantum number may assume the values of + /2 or -V2. Usually the sign of ms is represented by arrows, (t and ), or by the Greek letters a and (3. Thus, the wave function of an orbital is expressed as... 

There is a fourth quantum number that is necessary but does not result from the solution to the Schrodinger equation as we have written it. Rather, it results from a relativistic form of the equation. This is the spin quantum number, ms, which is needed for many-electron atoms and has values... 

The spin quantum number ms determines the angles possible between the axis of rotation and the external field as ... 

The spin quantum number, ms, determines the z-component of the spin angular momentum through the formula msh. For hydrogenic atomic orbitals, rns can only be 1/2. 

For Jf = 0, the spin operator is strictly dipolar, and the Zeeman Hamiltonian will induce a regular splitting of the quartet level, which is proportional to the spin quantum number, Ms- This case is illustrated in the left-hand panel of Fig. 7.5. Such cases will arise for an octahedral A state and also for the quartet spin-orbit level of a state. 

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